Electromagnetic Theory of Quartz. 153 



be produced when the direction of propagation is perpendi- 

 cular to the axis. Now in the ordinary theory of double 

 refraction, as developed by Maxwell, the electromotive force 

 is connected with the electric displacement by the three equa- 

 tions 



P = 4tt//K 1 , Q = 47n7/K 2 , R = 4ttA/K 8 , 



where K v , K 2 , K 3 are the three principal specific inductive 

 capacities. We shall now show that in a crystalline medium, 

 such as has been described above, rotatory polarization may 

 be accounted for by assuming that 



P = 4tt/;/K 1 +p 3 y-p 2 h, "J 



Q = 4:7rglK 2 +pji-p 3 f,\ (i) 



R = 477/^3+^/-^,) 



where p u p 2 , pz are constants. 



This assumption supposes that when electromotive force 

 acts upon the medium, it produces electric displacement in a 

 direction perpendicular to itself; and that the force depends 

 not only upon the actual displacement, but also upon the rate 

 at which it is taking place. 



The equations of electromotive force in terms of the electro- 

 magnetic momentum are ; 



P=-F-df/dxA 



Q=-a-df/dA (2) 



wiience 



da __ dH dQ 



dt dy dz 

 _db_dF_ dR 



dt~dz dx 

 _dc_ dQ_d? 



dt dx dy 



But if we assume that the magnetic permeability of the 

 medium is the same in all directions, we have 



W^=-J^-|), . (4) 



d 



i 



with two similar equations 



= vT _«(f + ^ + ^\ . . (5) 



dx \dx dy dz f 



